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Wilcoxon Signed Rank Test for One Mean
What do you know about the Wilcoxon Signed Rank test? Many consider it to be a good alternative to the one-sample t test, especially for non-normal data. Did you know that while it does not assume normal data, it does assume data from a symmetric distribution? Did you also know that it is not very robust for data from a skewed distribution? What does "not very robust" mean?
In the example shown here, the test accepts the null hypothesis that the median is equal to the known population median about 91% of the time for samples of size 30. However, notice that the acceptance rate falls as low as 80% for larger samples. When you run the test, you are assuming a 95% rate of acceptance. The distribution used in the simulation is highly skewed, which seems to have a worse affect the larger the sample size gets. This is why the test is considered to be "not very robust" for skewed data. You should use this test with extreme caution if you have skewed data, as the reported p value for the test could severely underestimate the actual p value.
We have developed a macro that allows you to check the acceptance rate for various degrees of skew, with a target sample size, and to change the number of samples used in the simulations.
|One-sample t test simulation|
|Wilcoxon test simulation|